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<H1>incremental_single_pair_shortest_path(+Graph, +DistanceArg, +SourceNode, +SinkNode, +Modified, -Path)</H1>
Computes short paths from a source to a sink node
<DL>
<DT><EM>Graph</EM></DT>
<DD>a graph structure
</DD>
<DT><EM>DistanceArg</EM></DT>
<DD>which argument of EdgeData to use as distance: integer
</DD>
<DT><EM>SourceNode</EM></DT>
<DD>source node number (integer)
</DD>
<DT><EM>SinkNode</EM></DT>
<DD>sink node number (integer)
</DD>
<DT><EM>Modified</EM></DT>
<DD>list of e/3 edge structures whose DistanceArg argument has been modified
</DD>
<DT><EM>Path</EM></DT>
<DD>Length-EdgeList structure
</DD>
</DL>
<H2>Description</H2>
<P>
    Incrementally computes shortest paths from SourceNode to SinkNode.
    Alternative paths are generated on backtracking. Fails if there is
    no path at all.
</P><P>
    DistanceArg refers to the graph's EdgeData information that was
    specified when the graph was constructed. If EdgeData is a simple
    number, then DistanceArg should be 0 and EdgeData will be taken
    as the length of the edge. If EdgeData is a compound data structure,
    DistanceArg should be a number between 1 and the arity of that
    structure and determines which argument of the EdgeData structure
    will be interpreted as the edge's length. Important: the distance
    information in EdgeData must be a positive number.
</P><P>
    If DistanceArg is given as -1, then any EdgeData is ignored and
    the length of every edge is assumed to be equal to 1.
</P><P>
    Modified is the list of e/3 edge structures whose DistanceArg
    argument has been modified since the last computation for this
    SourceNode.
</P><P>
    All paths returned will have the same length and will be shortest
    paths from SourceNode to SinkNode. Note that the solutions are not
    generated in any specific order.
</P><P>
    A resulting path is returned as a Length-EdgeList structure where
    Length is the length of the path and EdgeList is the path in
    reverse order, i.e. starting with the edge reaching SinkNode and
    ending with the edge starting from SourceNode.
    </P>
<H3>Modes and Determinism</H3><UL>
<LI>incremental_single_pair_shortest_path(+, +, +, +, +, -) is nondet
</UL>
<H3>Fail Conditions</H3>
There is no path from SourceNode to SinkNode
<H2>Examples</H2>
<PRE>
    ?- sample_graph(G), incremental_single_pair_shortest_path(G, 0, 1, M, P).
    P = 2 - [e(2, 3, 1), e(1, 2, 1)]
    </PRE>
<H2>See Also</H2>
<A HREF="../../lib/graph_algorithms/shortest_paths-4.html">shortest_paths / 4</A>, <A HREF="../../lib/graph_algorithms/single_pair_shortest_path-5.html">single_pair_shortest_path / 5</A>, <A HREF="../../lib/graph_algorithms/all_short_paths_as_edges-6.html">all_short_paths_as_edges / 6</A>, <A HREF="../../lib/graph_algorithms/all_short_paths_as_graph-6.html">all_short_paths_as_graph / 6</A>, <A HREF="../../lib/graph_algorithms/incremental_all_shortest_paths_as_edges-6.html">incremental_all_shortest_paths_as_edges / 6</A>, <A HREF="../../lib/graph_algorithms/incremental_all_shortest_paths_as_graph-6.html">incremental_all_shortest_paths_as_graph / 6</A>, <A HREF="../../lib/graph_algorithms/single_pair_short_path-6.html">single_pair_short_path / 6</A>, <A HREF="../../lib/graph_algorithms/single_pair_all_short_paths_as_graph-7.html">single_pair_all_short_paths_as_graph / 7</A>, <A HREF="../../lib/graph_algorithms/possible_path-7.html">possible_path / 7</A>
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